With Code Division Multiplexing/Code Division Multiple Access, multiplexing/multiple access is realized utilizing code orthogonality. With these systems, an orthogonal code functions as one type of key. A signal encoded by an orthogonal code is capable of being received only by an autocorrelation signal obtained in a case where the signal has been decoded by the same orthogonal code; it is not receivable with a cross-correlation signal obtained in a case where the signal has been decoded using a different orthogonal code. This technology is in wide practical use in electrical communication as a multiple access scheme for mobile telephones and wireless LANs.
Recent years have seen great activity in research and development of Optical Code Division Multiplexing (OCDM)/Optical Code Division Multiple Access (OCDMA) techniques, in which the above-mentioned Code Division Multiplexing/Code Division Multiple Access technology is applied to optical fiber communication systems. With OCDM/OCDMA, often use is made of optical encoding/optical decoding technology and orthogonal code suited to optical processing is desired. OCDM/OCDMA also employs Gold code and binary Hadamard code, which express a code by two phase states (example: 0, π) of a carrier wave generally used in electrical communication. With a Gold code, however, a long code is necessary in order to reduce cross-correlation signals (i.e., interference from other channels at the time of multiplexing/multiple access). Further, with a binary Hadamard code, code combinations in which the side lobes of cross-correlation signals cannot be reduced exist, and the binary Hadamard code can only be used in synchronous OCDM/OCDMA in which all multiplexed/multiple channels are synchronized. With the aim of solving these problems, use of 4-value codes for expressing codes by four phase states (example: 0, π/2, π, 3π/2) of a carrier wave is being studied. For example, refer to the following literature:    1. P. C Teh, M. Ibsen, H. Lee, P. Petropoulos, D. J. Richardson, “Demonstration of a Four-Channel WDM/OCDMA System Using 255-Chip 320-Gchip/s Quarternary Phase Coding Gratings”, IEEE PHOTONICS TECHNOLOGY LETTERS, vol. 14, no. 2, 2002    2. H Sotobayashi, W. Chujo K. Kitayama, “1.6 b/s/Hz 6.4-Tb/s QPSK-OCDM/WDM (4OCDM×40 WDM×40 Gb/s) Transmission Experiment Using Optical Hard Thresholding”, IEEE PHOTONICS TECHNOLOGY LETTERS, vol. 14, no. 4, 2002    3. S. Boztas, R. Hammons, P. V. Kumar, “4-Phase Sequences with Near-Optimum Correlation Properties,” IEEE Trans. Inform. Theory, vol. 38, no. 3, pp. 1101-1113, May 1992    4. L. C. Tran, J. Seberry, B. J. Wysocki, T. A. Wysocki, T. Xia and Ying Zhao, “Complex Orthogonal Sequences from Amicable Hadamard Matrices,” IEEE 59th Vehicular Technology Conference, Vol. 3, pp. 1490-1493, May 2004
Reference 1 reports on an OCDM system in which a four-value code (family A sequence code) referred to as a “family A sequence” proposed in Reference 2 is applied to OCDM and encoding/decoding to a family A sequence of code length 255 is performed by a superstructured fiber Bragg grating (SSFBG). However, since the device structure of an SSFBG is fixed when it is created, it is necessary to create one SSFBG with respect to one family A sequence in a case where the family A sequence code is used. Further, in order to increase the number of code sequences with the family A sequence code (i.e., in order to increase the number of multiplexed/multiple channels), a long code length is required. This makes it difficult to obtain a compact SSFBG-type encoder/decoder. In actuality, the SSFBG-type encoder/decoder utilized in Reference 1 has an overall length of 80 mm.
In Reference 3 also a 4-value code of code length 3 is utilized as an orthogonal code for OCDM. A code system, however, is not indicated. Further, Reference 4 reports on a computer search for converting a binary Hadamard code to obtain a multivalued Hadamard code. However, since a code cannot be obtained systematically, it is difficult in practice to obtain important information, such as the maximum number of code sequences and maximum cross-correlation value capable of being acquired in a certain code length. Further, it is required that the conversion matrix be found using a heuristic search algorithm, and as code length grows longer, it is difficult to finish the search in polynomial time.
Thus, a multivalued orthogonal code system for OCDM/OCDMA suited to encoding/decoding based upon optical processing, in which cross-correlation values are kept low, does not exist.